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Modular Forms, a Computational Approach
Pagexv(16 of 290)

Preface xv I would like to acknowledge the partial support of NSF Grant DMS 05- 55776. Gunnells was supported in part by NSF Grants DMS 02-45580 and DMS 04-01525. Notation and Conventions. We denote canonical isomorphisms by ∼ = and noncanonical isomorphisms by ≈. If V is a vector space and s denotes some sort of construction involving V , we let Vs denote the corresponding subspace and V s the quotient space. E.g., if ι is an involution of V , then V+ is Ker(ι − 1) and V + = V/Im(ι − 1). If A is a finite abelian group, then Ator denotes the torsion subgroup and A/tor denotes the quotient A/Ator. We denote right group actions using exponential notation. Everywhere in this book, N is a positive integer and k is an integer. If N is an integer, a divisor t of N is a positive integer such that N/t is an integer.